1. Field of the Invention
The present invention relates to a device and method of controlling a two-inertial resonant system and, more particularly, to a device for and method of controlling the vibrations of a two-inertial resonant system by using a state observer.
2. Description of the Related Art
A two-inertial resonant system, which has two moments of inertia, that is, a motor and a load connected to each other by the axis of a spring stiffness as shown in FIG. 1, is of great significance as a first approximate model for the spring joints and the flexible arms of a robot, space structures and the like.
FIG. 2 illustrates a dynamic model of such a two-inertial resonant system.
Referring to FIG. 2, a torsional torque T.sub.T generated by the difference in position between a motor and an actual load works as the load torque towards the motor. The difference between an electrical torque "u" and the torsional torque T.sub.T determines the motor's actual speed of revolution ".omega.".
The torsional torque T.sub.T, which acts as the load torque in the motor, is added to a disturbance torque T.sub.L externally applied, thereby determining the speed .omega..sub.L of the actual load.
Here, J is the motor's moment of inertia, T.sub.1 is the load's moment of inertia, and K is the stiffness coefficient. Further, .theta. is the position of the axis of the motor, .omega. is the speed of the motor, .theta..sub.L is the position of the load, .omega..sub.L is the speed of the load and T.sub.e is the motor torque.
In such a conventional two-inertial system, the position and the speed of the motor differ from those of the actual load in case of a sudden acceleration or deceleration since a motor is connected with the actual load via the axis of a spring stiffness.
Thus, the stability of the system may deteriorated deteriorate with vibrations produced when the motor's driving speed is controlled by the conventional method.
FIG. 3 is an illustration of a control system of a conventional two-inertial resonant system using a PI (Proportional Integral) controller, wherein reference numeral 20 denotes the two-inertial resonant system as shown in FIG. 2 and reference numeral 10 indicates a PI controller 10.
K.sub.P K.sub.I and K.sub.L are the speed proportional gain, the integral gain and the differential load acceleration feedback gain, respectively.
The speed feedback to the PI controller 10 is not the speed .omega..sub.L of the actual load to be controlled, but the speed .omega. of the motor detected by a sensor.
The speed .omega. of the motor detected by the sensor installed on the motor's axis is fed back to the PI controller 10, determining the speed difference from the reference speed .omega.* of the load. The PI controller 10 determines the sum of a component K.sub.P proportional to the speed difference and another component K.sub.L proportional to the integrated value of the speed difference.
The output of the PI controller 10 is applied as a torque command which is generated by the motor.
Under a torque "u" as a torque command generated by the motor, the speed .omega..sub.L of the actual load and the speed .omega. of the motor are both determined by the dynamics of the two-inertial resonant system as illustrated in FIG. 2. A sensor detects the motor's speed .omega., which will be fed back to the PI controller 10 for the calculation of the speed difference from the reference speed .omega.* of the load.
In the conventional method of controlling the vibrations of a two-inertial resonant system, the speed feedback to the PI controller 10 is not the speed .omega..sub.L of the actual load, which is to be controlled, but the speed .omega. of the motor detected by the sensor attached to the axis of the motor that is a driving component.
Furthermore, the motor and the actual load are connected with each other through the axis of a spring stiffness so that the position and the speed of the motor differ from those of the actual load in case of a sudden acceleration or deceleration. These differences in position and speed result in vibrations by the action of the torsional torque working as the load torque, as well as an increase in the system's instability.